Stability of a chain of phase oscillators

We study a chain of N + 1 phase oscillators with asymmetric but uniform coupling. This type of chain possesses 2 N ways to synchronize in so-called traveling wave states, i.e., states where the phases of the single oscillators are in relative equilibrium. We show that the number of unstable dimensions of a traveling wave equals the number of oscillators with relative phase close to π . This implies that only the relative equilibrium corresponding to approximate in-phase synchronization is locally stable. Despite the presence of a Lyapunov-type functional, periodic or chaotic phase slipping occurs. For chains of lengths 3 and 4 we locate the region in parameter space where rotations (corresponding to phase slipping) are present

Neurobiologically Inspired Control of Engineered Flapping Flight

This article presents a new control approach for engineered flapping flight with many interacting degrees of freedom. This paper explores the applications of neurobiologically inspired control systems in the form of Central Pattern Generators (CPG) to generate wing trajectories for potential flapping flight MAVs. We present a rigorous mathematical and control theoretic framework to design complex three dimensional motions of flapping wings. Most flapping flight demonstrators are mechanically limited in generating the wing trajectories. Because CPGs lend themselves to more biological examples of flight, a novel robotic model has been developed to emulate the flight of bats. This model has shoulder and leg joints totaling 10 degrees of freedom for control of wing properties. Results of wind tunnel experiments and numerical simulation of CPG-based flight control validate the effectiveness of the proposed neurobiologically inspired control approach

Energy Based Control System Designs for Underactuated Robot Fish Propulsion

In nature through millions of years of evolution fish and cetaceans have developed fast efficient and highly manoeuvrable methods of marine propulsion. A recent explosion in demand for sub sea robotics, for conducting tasks such as sub sea exploration and survey has left developers desiring to capture some of the novel mechanisms evolved by fish and cetaceans to increase the efficiency of speed and manoeuvrability of sub sea robots. Research has revealed that interactions with vortices and other unsteady fluid effects play a significant role in the efficiency of fish and cetaceans. However attempts to duplicate this with robotic fish have been limited by the difficulty of predicting or sensing such uncertain fluid effects. This study aims to develop a gait generation method for a robotic fish with a degree of passivity which could allow the body to dynamically interact with and potentially synchronise with vortices within the flow without the need to actually sense them. In this study this is achieved through the development of a novel energy based gait generation tactic, where the gait of the robotic fish is determined through regulation of the state energy rather than absolute state position. Rather than treating fluid interactions as undesirable disturbances and `fighting' them to maintain a rigid geometric defined gait, energy based control allows the disturbances to the system generated by vortices in the surrounding flow to contribute to the energy of the system and hence the dynamic motion. Three different energy controllers are presented within this thesis, a deadbeat energy controller equivalent to an analytically optimised model predictive controller, a $H_\infty$ disturbance rejecting controller with a novel gradient decent optimisation and finally a error feedback controller with a novel alternative error metric. The controllers were tested on a robotic fish simulation platform developed within this project. The simulation platform consisted of the solution of a series of ordinary differential equations for solid body dynamics coupled with a finite element incompressible fluid dynamic simulation of the surrounding flow. results demonstrated the effectiveness of the energy based control approach and illustrate the importance of choice of controller in performance

Biomimetic oscillating foil propulsion to enhance underwater vehicle agility and maneuverability

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2008Inspired by the swimming abilities of marine animals, this thesis presents "Finnegan the RoboTurtle", an autonomous underwater vehicle (AUV) powered entirely by four flapping foils. Biomimetic actuation is shown to produce dramatic improvements in AUV maneuvering at cruising speeds, while simultaneously allowing for agility at low speeds. Using control algorithms linear in the modified Rodrigues parameters to support large angle maneuvers, the vehicle is successfully controlled in banked and twisting turns, exceeding the best reported AUV turning performance by more than a factor of two; a minimum turning radius of 0.7BL, and the ability to avoid walls detected> 1.8BL ahead, are found for cruising speeds of 0.75BL/S, with a maximum heading rate of 400 / S recorded. Observations of "Myrtle", a 250kg Green sea turtle (Chelonia mydas) at the New England Aquarium, are detailed; along with steady swimming, Myrtle is observed performing 1800 level turns and rapidly actuating pitch to control depth and speed. Limb kinematics for the level turning maneuver are replicated by Finnegan, and turning rates comparable to those of the turtle are achieved. Foil kinematics which produce approximately sinusoidal nominal angle of attack trace are shown to improve turning performance by as much as 25%; the effect is achieved despite limited knowledge of the flow field. Finally, tests with a single foil are used to demonstrate that biomimetically inspired inline motion can allow oscillating foils utilizing a power/recovery style stroke to generate as much as 90% of the thrust from a power/power stroke style motion

Bio-Inspired Robotics

Modern robotic technologies have enabled robots to operate in a variety of unstructured and dynamically-changing environments, in addition to traditional structured environments. Robots have, thus, become an important element in our everyday lives. One key approach to develop such intelligent and autonomous robots is to draw inspiration from biological systems. Biological structure, mechanisms, and underlying principles have the potential to provide new ideas to support the improvement of conventional robotic designs and control. Such biological principles usually originate from animal or even plant models, for robots, which can sense, think, walk, swim, crawl, jump or even fly. Thus, it is believed that these bio-inspired methods are becoming increasingly important in the face of complex applications. Bio-inspired robotics is leading to the study of innovative structures and computing with sensory–motor coordination and learning to achieve intelligence, flexibility, stability, and adaptation for emergent robotic applications, such as manipulation, learning, and control. This Special Issue invites original papers of innovative ideas and concepts, new discoveries and improvements, and novel applications and business models relevant to the selected topics of ``Bio-Inspired Robotics''. Bio-Inspired Robotics is a broad topic and an ongoing expanding field. This Special Issue collates 30 papers that address some of the important challenges and opportunities in this broad and expanding field

Comparative Study of Forced Oscillators for the Adaptive Generation of Rhythmic Movements in Robot Controllers

International audienceThe interest of Central Pattern Generators (CPGs) in robot motor coordination is universally recognized so much so that a lot of possibilities on different scales of modeling are nowadays available. While each method obviously has its advantages and drawbacks, some could be more suitable for human-robot interactions. In this paper, we compare three oscillator models: Matsuoka, Hopf and Rowat-Selverston models. These models are integrated to a control architecture for a robotic arm and evaluated in simulation during a simplified handshaking interaction which involves constrained rhythmic movements. Furthermore, Heb-bian plasticity mechanisms are integrated to the Hopf and Rowat-Selverston models which can incorporate such mechanisms, contrary to the Matsuoka. Results show that the Matsuoka oscillator is subpar in all aspects and for the two others, that plasticity improves synchronization and leads to a significant decrease of the power consumption

Neuroinspired control strategies with applications to flapping flight

This dissertation is centered on a theoretical, simulation, and experimental study of control strategies which are inspired by biological systems. Biological systems, along with sufficiently complicated engineered systems, often have many interacting degrees of freedom and need to excite large-displacement oscillations in order to locomote. Combining these factors can make high-level control design difficult. This thesis revolves around three different levels of abstraction, providing tools for analysis and design. First, we consider central pattern generators (CPGs) to control flapping-flight dynamics. The key idea here is dimensional reduction - we want to convert complicated interactions of many degrees of freedom into a handful of parameters which have intuitive connections to the overall system behavior, leaving the control designer unconcerned with the details of particular motions. A rigorous mathematical and control theoretic framework to design complex three-dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show that flapping-flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of central pattern generator parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using a Hopf bifurcation, we show that tailless aircraft (inspired by bats) alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the central pattern generator network. Results of numerical simulation with a full six-degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach. Further, we present experimental micro aerial vehicle (MAV) research with low-frequency flapping and articulated wing gliding. The importance of phase difference control via an abstract mathematical model of central pattern generators is confirmed with a robotic bat on a 3-DOF pendulum platform. An aerodynamic model for the robotic bat based on the complex wing kinematics is presented. Closed loop experiments show that control dimension reduction is achievable - unstable longitudinal modes are stabilized and controlled using only two control parameters. A transition of flight modes, from flapping to gliding and vice-versa, is demonstrated within the CPG control scheme. The second major thrust is inspired by this idea that mode switching is useful. Many bats and birds adopt a mixed strategy of flapping and gliding to provide agility when necessary and to increase overall efficiency. This work explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of nonlinear switching limit cycles from our work on flapping flight. This level of abstraction has been found to be useful in many ways, but it also produces its own challenges. For example, we discuss death of oscillation which can occur for many limit-cycle controllers and the difficulty in incorporating fast, high-displacement reflex feedback. This leads us to our third major thrust - considering biologically realistic neuron circuits instead of a limit cycle abstraction. Biological neuron circuits are incredibly diverse in practice, giving us a convincing rationale that they can aid us in our quest for flexibility. Nevertheless, that flexibility provides its own challenges. It is not currently known how most biological neuron circuits work, and little work exists that connects the principles of a neuron circuit to the principles of control theory. We begin the process of trying to bridge this gap by considering the simplest of classical controllers, PD control. We propose a simple two-neuron, two-synapse circuit based on the concept that synapses provide attenuation and a delay. We present a simulation-based method of analysis, including a smoothing algorithm, a steady-state response curve, and a system identification procedure for capturing differentiation. There will never be One True Control Method that will solve all problems. Nature's solution to a diversity of systems and situations is equally diverse. This will inspire many strategies and require a multitude of analysis tools. This thesis is my contribution of a few

Modeling, Control and Locomotion Planning of an Anguilliform Fish Robot

Ph.DDOCTOR OF PHILOSOPH

Methodological Remarks on CPG-Based Control of Flapping Flight

This paper is a companion to Chung and explores the applications of neurobiologically inspired control systems in the form of Central Pattern Generators (CPG) to control flapping flight dynamics. We introduce two-layer CPGs to mimic current hypotheses of mammalian studies. It is shown that symmetry breaking to initiate and recover from a turning maneuver is an effective control strategy. Attempts at dissociating slow dynamics are shown and preliminary comparisons of wing motions between biological fliers and artificial CPG networks are made